What Is a Binomial Random Variable?

A binomial random variable is a unique type of discrete random variable that counts the frequency of occurrence of a particular event in a fixed number of trials. Several conditions must be met for a variable to be declared a binomial random variable. Two of the conditions are that the number of trials must be fixed and that each trial has only two possible outcomes.

Other mandatory conditions are that the probability of a success or a failure in each trial must be the same for all the trails, and the outcome of each trial must be independent of the other trials. The binomial random variable has a probability distribution referred to as the binomial distribution.

The mean of the binomial distribution is given by n * P, while its variance is the result of n * P * (1 - P), and the standard deviation is the square root of the variance. The binomial probability, which is the probability of a binomial experiment resulting in X number of successes, can be calculated using the binomial formula, which is written as, b(x; n, P) = {n! / [ X! (n - x)! ]} * P^x * (1 - P)^n - x.